def main(argv):
hhModel = HodgkinAndHuxleyModel(i=None)
vs = np.arange(10, 100, 1e-3)
tauMs = hhModel._tauM(v=vs)
mCBase = min(tauMs)
mCAmp = max(tauMs)-mCBase
mVMax = vs[np.argmax(tauMs)]
mSigma = abs(mVMax-vs[np.argmin(abs((tauMs-mCBase)-(max(tauMs)-mCBase)*np.exp(-1)))])
tauMsApproxFun = lambda v: mCBase+mCAmp*np.exp(-(mVMax-v)**2/mSigma**2)
tauMsApprox = tauMsApproxFun(v=vs)
# begin delete
refValue = mCBase+mCAmp*np.exp(-1)
tauMAtMVMaxPlusMSigma = hhModel._tauN(v=mVMax+mSigma)
tauMApproxAtMVMaxPlusMSigma = tauMsApproxFun(v=mVMax+mSigma)
closeToZero1 = abs(tauMAtMVMaxPlusMSigma-refValue)
closeToZero2 = abs(tauMApproxAtMVMaxPlusMSigma-refValue)
# end delete
plt.figure()
plt.plot(vs, tauMs, label=r"$\tau_M$(v)")
plt.plot(vs, tauMsApprox, label=r"$\hat{\tau}_M$(v)")
plt.axhline(y=min(tauMs[vs>60]))
plt.xlabel("V (mv)")
plt.ylabel("Time Constant")
plt.legend(loc="upper right")
plt.show()
pdb.set_trace()
def main(argv):
figFilename = "figures/fig2-13.eps"
def i(t):
return 0.0
hhModel = HodgkinAndHuxleyModel(i=i)
v = np.arange(-40, 100, .1)
nInf = hhModel._nInf(v=v)
mInf = hhModel._mInf(v=v)
hInf = hhModel._hInf(v=v)
tauN = hhModel._tauN(v=v)
tauM = hhModel._tauM(v=v)
tauH = hhModel._tauH(v=v)
f, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(v, nInf, label=r"$n_\infty$(V)")
ax1.plot(v, mInf, label=r"$m_\infty$(V)")
ax1.plot(v, hInf, label=r"$h_\infty$(V)")
ax1.legend(loc="lower right")
ax1.set_xlabel("V (mv)")
ax1.set_ylabel("Probability")
ax2.plot(v, tauN, label=r"$\tau_n$(V)")
ax2.plot(v, tauM, label=r"$\tau_m$(V)")
ax2.plot(v, tauH, label=r"$\tau_h$(V)")
ax2.legend(loc="upper right")
ax2.set_xlabel("V (mv)")
ax2.set_ylabel("Time (ms)")
plt.savefig(figFilename)
pdb.set_trace()
def main(argv):
i0 = 0.0
v0 = 0.0
n0 = 0.31767691406070614
m0 = 0.052932485257253123
h0 = 0.5961207535084404
t0 = 0.0
t1 = 2.0
t2 = 10.0
tf = 20.0
dt = 1e-5
nVOneHalf = -45.0,
iPulse1Strength = 10.0
iPulse2Strength = 25.0
iPulseWidth = 0.25
traceCol = 'grey'
traceMarker = '.'
def i(t):
return(i0)
nTSteps = round((tf-t0)/dt)
times = np.empty(nTSteps+1)
hhModel = HodgkinAndHuxleyModel(i=i)
integrator = ode(hhModel.deriv).set_integrator('vode', max_step=dt)
y0 = np.array([v0, n0, m0, h0])
integrator.set_initial_value(y0, t0)
ys = np.empty((4, nTSteps+1))
ys[:, 0] = y0
t = t0
step = 0
successfulIntegration = True
while successfulIntegration and step<nTSteps:
step = step+1
if step%1000==0:
print('Processing time %.05f out of %.02f' % (t, tf))
sys.stdout.flush()
integrator.integrate(t+dt)
t = integrator.t
y = integrator.y
times[step] = t
ys[:, step] = y
inputCurrent = np.empty(len(times))
for j in xrange(len(times)):
inputCurrent[j] = i(t=times[j])
resultsFilename = 'results/integrationHodgkinAndHuxley_noInput.npz'
np.savez(resultsFilename, times=times, ys=ys, inputCurrent=inputCurrent)
plt.plot(times, ys[0, :])
plt.grid()
plt.xlabel('Time (secs)')
plt.ylabel('Voltage (mv)')
plt.savefig('figures/voltageTraceIntegrationHodgkinAndHuxley_noInput.eps')
plt.show()
pdb.set_trace()
def main(argv):
vs = np.arange(-40, 100, .1)
hhModel = HodgkinAndHuxleyModel(i=None)
approxHHModel = ApproxHodgkinAndHuxleyModel(i=None)
nInfs = hhModel._nInf(v=vs)
approxNInfs = approxHHModel._nInf(v=vs)
mInfs = hhModel._mInf(v=vs)
approxMInfs = approxHHModel._mInf(v=vs)
hInfs = hhModel._hInf(v=vs)
approxHInfs = approxHHModel._hInf(v=vs)
tauNs = hhModel._tauN(v=vs)
approxTauNs = approxHHModel._tauN(v=vs)
tauMs = hhModel._tauM(v=vs)
approxTauMs = approxHHModel._tauM(v=vs)
tauHs = hhModel._tauH(v=vs)
approxTauHs = approxHHModel._tauH(v=vs)
plt.subplot(2, 1, 1)
plt.plot(vs, nInfs, label=r"$n_\infty$(v)")
plt.plot(vs, approxNInfs, label=r"$\tilde{n}_\infty$(v)")
plt.plot(vs, mInfs, label=r"$m_\infty$(v)")
plt.plot(vs, approxMInfs, label=r"$\tilde{m}_\infty$(v)")
plt.plot(vs, hInfs, label=r"$h_\infty$(v)")
plt.plot(vs, approxHInfs, label=r"$\tilde{h}_\infty$(v)")
plt.ylabel("Proability Open")
plt.legend()
plt.subplot(2, 1, 2)
plt.plot(vs, tauNs, label=r"$\tau_n$(v)")
plt.plot(vs, approxTauNs, label=r"$\hat{\tau}_n$(v)")
plt.plot(vs, tauMs, label=r"$\tau_m$(v)")
plt.plot(vs, approxTauMs, label=r"$\hat{\tau}_m$(v)")
plt.plot(vs, tauHs, label=r"$\tau_h$(v)")
plt.plot(vs, approxTauHs, label=r"$\hat{\tau}_h$(v)")
plt.xlabel("Voltage (mV)")
plt.ylabel("Time Constant")
plt.legend()
plt.show()
def main(argv):
hhModel = HodgkinAndHuxleyModel(i=None)
vs = np.arange(-40, 100, 1e-3)
nInfs = hhModel._nInf(v=vs)
nVOneHalf = vs[np.argmin(np.abs(nInfs - .5))]
nK = -(vs[np.argmin(np.abs(nInfs - 1.0 / (1 + np.exp(1))))] - nVOneHalf)
nInfsApproxFunc = lambda v: 1.0 / (1 + np.exp((nVOneHalf - v) / nK))
nInfsApprox = nInfsApproxFunc(v=vs)
mInfs = hhModel._mInf(v=vs)
mVOneHalf = vs[np.argmin(np.abs(mInfs - .5))]
mK = -(vs[np.argmin(np.abs(mInfs - 1.0 / (1 + np.exp(1))))] - mVOneHalf)
mInfsApproxFunc = lambda v: 1.0 / (1 + np.exp((mVOneHalf - v) / mK))
mInfsApprox = mInfsApproxFunc(v=vs)
hInfs = hhModel._hInf(v=vs)
hVOneHalf = vs[np.argmin(np.abs(hInfs - .5))]
hK = -(vs[np.argmin(np.abs(hInfs - 1.0 / (1 + np.exp(1))))] - hVOneHalf)
hInfsApproxFunc = lambda v: 1.0 / (1 + np.exp((hVOneHalf - v) / hK))
hInfsApprox = hInfsApproxFunc(v=vs)
tauNs = hhModel._tauN(v=vs)
nCBase = min(tauNs)
nCAmp = max(tauNs) - nCBase
nVMax = vs[np.argmax(tauNs)]
nSigma = abs(
nVMax -
vs[np.argmin(abs((tauNs - nCBase) -
(max(tauNs) - nCBase) * np.exp(-1)))])
tauNsApproxFun = lambda v: nCBase + nCAmp * np.exp(-(nVMax - v)**2 / nSigma
**2)
tauNsApprox = tauNsApproxFun(v=vs)
# tauMs = hhModel._tauM(v=vs)
# mCBase = min(tauMs)
# mCAmp = max(tauMs)-mCBase
# mVMax = vs[np.argmax(tauMs)]
# mSigma = abs(mVMax-vs[np.argmin(abs((tauMs-mCBase)-(max(tauMs)-mCBase)*np.exp(-1)))])
# tauMsApproxFun = lambda v: mCBase+mCAmp*np.exp(-(mVMax-v)**2/mSigma**2)
# tauMsApprox = tauMsApproxFun(v=vs)
# begin delete
refValue = mCBase + mCAmp * np.exp(-1)
tauMAtMVMaxPlusMSigma = hhModel._tauN(v=mVMax + mSigma)
tauMApproxAtMVMaxPlusMSigma = tauMsApproxFun(v=mVMax + mSigma)
closeToZero1 = abs(tauMAtMVMaxPlusMSigma - refValue)
closeToZero2 = abs(tauMApproxAtMVMaxPlusMSigma - refValue)
pdb.set_trace()
# end delete
tauHs = hhModel._tauH(v=vs)
hCBase = min(tauHs)
hCAmp = max(tauHs) - hCBase
hVMax = vs[np.argmax(tauHs)]
hSigma = abs(
hVMax -
vs[np.argmin(abs((tauHs - hCBase) -
(max(tauHs) - hCBase) * np.exp(-1)))])
tauHsApproxFun = lambda v: hCBase + hCAmp * np.exp(-(hVMax - v)**2 / hSigma
**2)
tauHsApprox = tauHsApproxFun(v=vs)
plt.plot(vs, nInfs, label=r"$n_{\infty}$(v)")
plt.plot(vs, nInfsApprox, label=r"$\hat{n}_{\infty}$(v)")
plt.plot(vs, mInfs, label=r"$m_{\infty}$(v)")
plt.plot(vs, mInfsApprox, label=r"$\hat{m}_{\infty}$(v)")
plt.plot(vs, hInfs, label=r"$h_{\infty}$(v)")
plt.plot(vs, hInfsApprox, label=r"$\hat{h}_{\infty}$(v)")
plt.xlabel("V (mv)")
plt.ylabel("Probability")
plt.legend(loc="lower right")
plt.figure()
plt.plot(vs, tauNs, label=r"$\tau_N$(v)")
plt.plot(vs, tauNsApprox, label=r"$\hat{\tau}_N$(v)")
# plt.plot(vs, tauMs, label=r"$\tau_M$(v)")
# plt.plot(vs, tauMsApprox, label=r"$\hat{\tau}_M$(v)")
plt.plot(vs, tauHs, label=r"$\tau_H$(v)")
plt.plot(vs, tauHsApprox, label=r"$\hat{\tau}_H$(v)")
plt.xlabel("V (mv)")
plt.ylabel("Time Constant")
plt.legend(loc="upper right")
plt.show()
pdb.set_trace()